Consider ·an astronaut trapped in space, isolated from surrounding. He can reach his spacecraft if some velocity is gained by him somehow. Suddenly he realises that he has got a small pencil in his pocket. How can he acquire velocity (momentum) ?
We take the system to consist of the astronaut and the pencil as shown in Fig. 4.4. We assign the positive direction of the x-axis to be the direction of throw. The gravitational force acts on the $Y5tem, which indeed is external force. However, this force is directed along the y-axis, it will not change momentum along x-axis. we· can thus apply the conservation of momentum to this system. What happens to the force exerted by the astronaut on the pencil while throwing it?
`m_(a) vecV_(ai) + m_(p)vecV _("pi") = m_(a) vecV _(af) + m_(p)vecV _(pf)
0 + 0 = M_(a)vecV_(af) + m_(p)vecV _(pf)
vecV_(af) =-(m_(P)vec_(pf))/m_(a)`
The negative sign indicates that the astronaut moves in the direction opposite. to the direction of motion of the pencil.